Finite Group Databasebeta

← C131×#7357 #45693241

Subgroups — C131×#7357 #45693241

Order 33536.

222 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1962×C131C211yesmaximal, characteristic
2#1327×C131C212yesmaximal, complemented
3#532×C131C411yescharacteristic
4#423×C131C2211yescharacteristic
5C2×#104×C131—22no—
6C43×C131C411yescharacteristic
7#349×C131—22no—
8C2×#41×C131—21no—
9C2×M16×C131D412yes—
10C4⋊Q8×C131C811yescharacteristic
11#127×C131C811yescharacteristic
12#124×C131—21no—
13#121×C131—41no—
14C4×D4×C131—41no—
15C2×C42×C131—21no—
16C2×C42×C131—41no—
17C2×C42×C131C2×C411yescharacteristic
18M32×C131—42no—
19C4⋊C8×C131—41no—
20#104×C131—44no—
21#41×C131—42no—
22#41×C131—42no—
23C2×Q8×C131—21no—
24C2×D4×C131—21no—
25C2×D4×C131—41no—
26C2×D4×C131—41no—
27C22×C4×C131—21no—
28C22×C4×C131—41no—
29C22×C4×C131—41no—
30C22×C4×C131C22⋊C411yescharacteristic
31M16×C131—42no—
32C2×C8×C131—22no—
33C4⋊C4×C131—41no—
34C22⋊C4×C131—42no—
35C42×C131—21no—
36C42×C131—22no—
37C42×C131—41no—
38C42×C131—44no—
39C42×C131C2×C811yescharacteristic
40C42×C131M1611yescharacteristic
41C16×C131—82no—
42C23×C131—41no—
43C23×C131#10011yescharacteristic
44Q8×C131—42no—
45D4×C131—42no—
46D4×C131—82no—
47D4×C131—82no—
48C2×C4×C131—21no—
49C2×C4×C131—21no—
50C2×C4×C131—21no—
51C2×C4×C131—21no—
52C2×C4×C131—42no—
53C2×C4×C131—42no—
54C2×C4×C131—44no—
55C2×C4×C131—41no—
56C2×C4×C131—81no—
57C2×C4×C131—81no—
58C2×C4×C131C22⋊C811yescharacteristic
59C2×C4×C131#9911yescharacteristic
60C8×C131—42no—
61C22×C131—21no—
62C22×C131—41no—
63C22×C131—82no—
64C22×C131—81no—
65C22×C131#32311yescharacteristic
66C4×C131—22no—
67C4×C131—21no—
68C4×C131—41no—
69C4×C131—44no—
70C4×C131—81no—
71C4×C131#35311yescharacteristic
72C4×C131#35511yescharacteristic
73C2×C131—21no—
74C2×C131—41no—
75C2×C131—161no—
76C2×C131#131811yescharacteristic
77#7357C13111yesmaximal, characteristic, direct product factor, Sylow
78C131#735711yescharacteristic, direct product factor, Sylow
79#1962C2×C13111yescharacteristic
80#1327C2×C13112yescomplemented
81#532C4×C13111yescharacteristic
82#423C22×C13111yescharacteristic
83C2×#104—22no—
84C43C4×C13111yescharacteristic
85#349—22no—
86C2×#41—21no—
87C2×M16D4×C13112yes—
88C4⋊Q8C8×C13111yescharacteristic
89#127C8×C13111yescharacteristic
90#124—21no—
91#121—41no—
92C4×D4—41no—
93C2×C42—21no—
94C2×C42—41no—
95C2×C42C2×C4×C13111yescharacteristic
96M32—42no—
97C4⋊C8—41no—
98#104—44no—
99#41—42no—
100#41—42no—
101C2×Q8—21no—
102C2×D4—21no—
103C2×D4—41no—
104C2×D4—41no—
105C22×C4—21no—
106C22×C4—41no—
107C22×C4—41no—
108C22×C4C22⋊C4×C13111yescharacteristic
109M16—42no—
110C2×C8—22no—
111C4⋊C4—41no—
112C22⋊C4—42no—
113C42—21no—
114C42—22no—
115C42—41no—
116C42—44no—
117C42C2×C8×C13111yescharacteristic
118C42M16×C13111yescharacteristic
119C16—82no—
120C23—41no—
121C23#100×C13111yescharacteristic
122Q8—42no—
123D4—42no—
124D4—82no—
125D4—82no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—44no—
133C2×C4—41no—
134C2×C4—81no—
135C2×C4—81no—
136C2×C4C22⋊C8×C13111yescharacteristic
137C2×C4#99×C13111yescharacteristic
138C8—42no—
139C22—21no—
140C22—41no—
141C22—82no—
142C22—81no—
143C22#323×C13111yescharacteristic
144C4—22no—
145C4—21no—
146C4—41no—
147C4—44no—
148C4—81no—
149C4#353×C13111yescharacteristic
150C4#355×C13111yescharacteristic
151C2—21no—
152C2—41no—
153C2—161no—
154C2#1318×C13111yescharacteristic
subgroupG/H
centerC4×C131#353
commutatorC42C2×C8×C131
Frattini, cosocle#423C22×C131
socleC2×C131#1318
prime radical#532×C131C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #423×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #1327×C131C2semidirect
77. #7357C131direct (N × H)
78. C131#7357direct (N × H)
80. #1327C2×C131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#1962×C1312
#1327×C1312
#7357131